Early detail-preserving mesh deformation techniques were based multi-resolution techniques. Casting mesh deformation as an energy minimization problem allowed more global and complex deformation. Typically, the energy functions used in these techniques contain terms to preserve detail (often through Laplacian coordinates), as well as position-constraint terms to allow for direct manipulation. Additional suggestions include introducing more terms in the optimization (e.g., volume or skeleton constraints) as a convenient way to design more complex deformation with ease, without the traditional shearing artifacts appearing in large scale deformation. However, these existing techniques do not currently scale, as the optimizations involved are often nonlinear and require slow-converging Gauss-Newton iterations. These methods rely on a good initial guess to converge to a correct solution and are generally slow to achieve convergence.
A technique, the graphics industry uses is Skeleton Sub-space Deformation (SSD) and several variants as a natural and efficient representation for character animation in games and films. However, SSD and these variants restrict deformation to a particular subspace for efficiency, causing shortcomings such as a characteristic “collapsing joint” defect as well as the tedious tweaking of vertex weights. Despite significant improvements to allow for easier mesh manipulation and interpolation, these rigging tools do not allow for rapid design of complex deformation. Rigging is not very effective as the user has to manipulate a properly-designed skeleton to deform the posture of a character. Unfortunately, moving the skeleton of a “skinned mesh” causes the mesh to follow with unpleasant consequences. Thus, applying skinning (or “binding”) matches the fine-detail shape of the mesh to the positions of the skeletons based on functional optimization and differential coordinates. While these approaches to mesh deformation have pros and cons, neither allows for interactive design of high-quality, large-scale or fine-scale deformation of detailed meshes.
To further illustrate the problems of skinned mesh deformation, deformation energy involving variables, such as vertex positions and bone transformations, are delicate to formulate. Traditional Inverse Kinematics (IK) allow efficient large-scale deformation of skeletal figures through optimization of an energy function in the null space of constraints. IK constraints are highly nonlinear, often involving inequalities. Furthermore, existing mesh deformation solvers used to solve nonlinear constraints, even with multigrid strategies, have lead to poor performance. Thus, mesh deformation techniques have not provided interactive design tools and a satisfying user experience.